I. Description of Formal Mathematics -- ยง 1. Terms and relations -- ยง 2. Theorems -- ยง 3. Logical theories -- ยง 4. Quantified theories -- ยง 5. Equalitarian theories -- Appendix. Characterization of terms and relations -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Exercises for ยง 4 -- Exercises for ยง 5 -- Exercises for the Appendix -- II. Theory of Sets -- ยง 1. Collectivizing relations -- ยง 2. Ordered pairs -- ยง 3. Correspondences -- ยง 4. Union and intersection of a family of sets -- ยง 5. Product of a family of sets -- ยง 6. Equivalence relations -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Exercises for ยง 4 -- Exercises for ยง 5 -- Exercises for ยง 6 -- III. Ordered Sets, Cardinals, Integers -- ยง 1. Order relations. Ordered sets -- ยง 2. Well-ordered sets -- ยง 3. Equipotent sets. Cardinals -- ยง 4. Natural integers. Finite sets -- ยง 5. Properties of integers -- ยง 6. Infinite sets -- ยง 7. Inverse limits and direct limits -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Exercises for ยง 4 -- Exercises for ยง 5 -- Exercises for ยง 6 -- Exercises for ยง 7 -- Historical Note on ยง 5 -- IV. Structures -- ยง 1. Structures and isomorphisms -- ยง 2. Morphisms and derived structures -- ยง 3. Universal mappings -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Historical Note on Chapters I-IV -- Summary of Results -- ยง 1. Elements and subsets of a set -- ยง 2. Functions -- ยง 3. Products of sets -- ยง 4. Union, intersection, product of a family of sets -- ยง 5. Equivalence relations and quotient sets -- ยง 6. Ordered sets -- ยง 7. Powers. Countable sets -- ยง 8. Scales of sets. Structures -- Index of notation -- Index of terminology -- Axioms and schemes of the theory of sets

1. Mathematics
2. Mathematical logic
3. Mathematics
4. Mathematical Logic and Foundations